We introduce CESRBDDs, a form of binary decision diagrams (BDDs) that can exploit reduction opportunities beyond those allowed by reduced ordered BDDs (elimination of redundant nodes), zero-suppressed BDDs (elimination of “high-zero” nodes), and recent proposals merging the two (chained or tagged BDDs). CESRBDDs also incorporate complemented edges, thus never store both the encoding of a function and of its complement. We prove that CESRBDDs are canonical and show how their storage requirements and computational efficiency compare very favorably against previous alternatives, both theoretically and experimentally, using an extensive set of benchmarks. Another advantage of CESRBDDs over chained or tagged BDDs is that their nodes only require one byte to store reduction and complement information.